Analog to Analog Encoding

Analog signals are modulated because:

• Higher frequency gives more efficient transmission.
• Permits frequency division multiplexing.

Modulations

AM

Short for Amplitude Modulation. Amplitude of the carrier signal is varied according to information. Frequency of the carrier signal is much greater than the input message signal frequency.

$$s(t) = A_c (1 + km(t)) \cos(\omega_c t)$$

Here:

• $A_c$: Amplitude of the carrier signal
• $k$: Modulation index
• $m(t)$: Modulation signal
• $\omega_c$: Angular frequency of the carrier signal

The carrier signal would be given by: $c(t) = A_c \cos(\omega_c t)$. $$

$A_c(1 + km(t))$ is called the envelope of the signal. $$

FM

Short for Frequency Modulation. Frequency of the carrier signal is varied according to information.

$$s(t) = A_c\cos(\omega_c t + \theta(t))$$

Here:

$$\theta(t) = 2\pi \Delta_f \int_{-\infty}^t m(\tau) \text{d}\tau$$

• $\Delta_p$: Phase modulation index
• $A_c$: Amplitude of the carrier signal
• $m(t)$: Modulation signal
• $\omega_c$: Angular frequency of the carrier signal

PM

Short for Phase Modulation. Phase of the carrier signal is varied according to information.

$$s(t) = A_c\cos(\omega_c t + \theta(t))$$

Here $\theta(t) = \Delta_p m(t)$ and:

• $\Delta_p$: Phase modulation index
• $A_c$: Amplitude of the carrier signal
• $m(t)$: Modulation signal
• $\omega_c$: Angular frequency of the carrier signal